Self-injection locking for low-power low-phase noise oscillators

ABSTRACT

For producing a low-power, low-phase noise oscillating signal using a self-injection locking oscillator, examples include: producing, using an oscillator, a signal having a base frequency component and an Nth harmonic component, in which N is a selected integer and N&gt;1; filtering the signal through a bandpass filter with Q factor ≥5, the filter configured to pass the Nth harmonic component as a filtered Nth harmonic component; and injecting the filtered Nth harmonic component into the oscillator to self-injection lock the base frequency of the signal.

BACKGROUND

The present application relates to oscillator circuits, and moreparticularly to low-power, low-phase noise clock signal generators.

Note that the points discussed below may reflect the hindsight gainedfrom the disclosed inventive scope, and are not necessarily admitted tobe prior art.

A variety of approaches exist for generating electronic device clocksignals, with varying types of limitations. For example, quartz crystaloscillators may be useful for frequencies under about 200 MHz, and canprovide highly stable frequency outputs with very little phase noise,but can be sensitive to temperature and vibration and may face size orfrequency limitations. LC oscillators connected to a divider, as well asMEMS (micro-electromechanical systems) oscillators such as bulk acousticwave (BAW) resonators, can also be used to produce situationally usefulclocks. However, divider circuits are generally power-hungry because oftransitions at the oscillator frequency, and MEMS oscillators atrelatively low frequencies (e.g., 200 MHz to 1 GHz) may be too large tofit within a device area budget.

FIG. 2A shows an example of a locking range graph 200 of an oscillator.For an oscillator operating at a particular base frequency ω₀ 202, therange of amplitudes and frequencies of a signal injected into which willcause the oscillator to injection lock (explained below) is called theoscillator's “locking range” 204. When a first oscillator is disturbedby a second oscillator operating at a nearby frequency, and the couplingis strong enough and the frequencies near enough, the second oscillatorcan “capture” the first oscillator, causing the first oscillator tooscillate at an approximately identical frequency to the secondoscillator. This is injection locking. That is, for first and secondoscillators with different operating frequencies, there is a minimumamplitude of the second oscillator signal that will cause the firstoscillator to injection lock to the second oscillator's operatingfrequency. Beneath that minimum amplitude, there is a region 206 wherethe first oscillator will not lock. The minimum amplitude for injectionlocking is primarily determined by the operating frequencies of thefirst and second oscillators, the difference between those frequencies,and the respective structures of the oscillators. While the secondoscillator's signal continues to be injected into the first oscillatorat a sufficient amplitude, the first oscillator will continue to outputa signal at (approximately) the operating frequency of the secondoscillator. See, e.g., FIG. 5 regarding injection locking, andparticularly regarding the time-dependent sensitivity of an oscillatorto an injected signal.

Injection locking can also occur when the first oscillator is operatingat a frequency nearby a harmonic of the second oscillator's operatingfrequency; or when a harmonic of the first oscillator's operatingfrequency is nearby the second oscillator's operating frequency; or whena harmonic of the first oscillator's operating frequency is near aharmonic of the second oscillator's operating frequency.

Output of an oscillator can be input back into the oscillator to induceself-injection locking. Self-injection locking induced on an oscillatorby a sufficiently group-delayed oscillator output signal can result insignificantly lowering the phase noise in the self-injection lockedoscillator output signal.

FIG. 2B schematically shows an example of a self-injection locking phaselocked loop 208 (SILPLL). See L. Zhang, A. Daryoush, A. Poddar and U.Rohde, “Oscillator phase noise reduction using self-injection locked andphase locked loop (SILPLL),” 2014 IEEE International Frequency ControlSymposium (FCS), Taipei, 2014, pp. 1-4, which is incorporated herein byreference. As shown, an SILPLL 208 comprises a voltage controlledoscillator 210 (VCO), a self-phase locked loop 212 (SPLL), a 1 km to 3km optical fiber cable 214 used to introduce a group delay so thatinjection locking will reduce phase noise in the VCO 210 output, and aself-injection locking (SIL) block 216 that injects the group-delayedVCO 210 output back into the VCO 210, connected in looped series. Theoutput of the VCO 210 comprises the output of the SILPLL 208 (through a10 dB coupler), as well as being fed back to the SPLL 212. (MZM standsfor Mach-Zehnder modulator.) Phase noise improvement in an SILPLL 208 asshown is proportional to the delay time introduced by the optical fiber214. As a result of the length of the optical fiber 214 required toachieve phase noise improvement, there is a floor on the device arearequired by an SILPLL 208 as shown that achieves significant phase noisereductions in the VCO 210 output.

FIG. 2C schematically shows an example of a self-injection-lockingoscillator 218. See Heng-Chia Chang, “Stability analysis ofself-injection-locked oscillators,” IEEE Transactions on MicrowaveTheory and Techniques, vol. 51, no. 9, pp. 1989-1993, September 2003;and Heng-Chia Chang, “Phase noise in self-injection-lockedoscillators—theory and experiment,” in IEEE Transactions on MicrowaveTheory and Techniques, vol. 51, no. 9, pp. 1994-1999, September 2003;both of which are incorporated herein by reference. An output signal 220from an oscillator 222 is directed by a circulator 224 to a delay line,high Q resonator, or amplifier 226 (for example, a microwave resonantcavity measuring approximately five to six cm in length and containing astanding wave) tuned to the same frequency as the oscillator 222. (Thepictured power divider and spectrum analyzer are not relevant here.) Thegroup-delayed output 228 of the delay line, high Q resonator, oramplifier 226 is then directed by the circulator 224 back to theoscillator 222. The group-delayed output 228 is then injected into theoscillator 222 so that the oscillator 222 locks to its own,group-delayed output signal 228.

Injection locking can also be used with a ring oscillator to providefrequency division. FIG. 2D shows an example of a transistor-leveldiagram of a divide-by-three injection locked frequency divider 230(ILFD). See X. Yi, C. C. Boon, M. A. Do, K. S. Yeo and W. M. Lim,“Design of Ring-Oscillator-Based Injection-Locked Frequency DividersWith Single-Phase Inputs,” IEEE Microwave and Wireless ComponentsLetters, vol. 21, no. 10, pp. 559-561, October 2011, which isincorporated herein by reference. The circuit shown in FIG. 2C is basedon a 3-stage ring oscillator 232.

As shown in FIG. 2D, an input signal RF is connected through a capacitorand an inductor (Bias Tee) to an Injection Circuit node V_(inj). V_(inj)biases the gates of three transistors M₁, M₂ and M₃, which are connectedsource to drain M₃ to M₂ to M₁ to M₃. The source of M₁ is connected tonode V₁, the source of M₂ is connected to node V₂, and the source of M₃is connected to node V₃. C_(p,1), C_(p,2) and C_(p,3) are parasiticcapacitances of nodes V₁, V₂ and V₃, respectively. A transistor 234 hasits source connected to V_(DD), its drain connected to node V₁, and isbiased by oscillator 232 input voltage V_(b). V_(b) is a control voltagefor the ring oscillator 232; V_(b) controls the frequency of the ringoscillator 232 by increasing or decreasing the current available to eachstage through corresponding PMOS transistors 234, 238, 242. A transistor236 has its source connected to ground, its drain connected to node V₁,and its bias connected to node V₃ and the source of M₃. A transistor 238has its source connected to V_(DD), its drain connected to node V₂, andis biased by oscillator 232 input voltage V_(b). A transistor 240 hasits source connected to ground, its drain connected to node V₂, and itsbias connected to node V₁. A transistor 242 has its source connected toV_(DD), its drain connected to node V₃, and is biased by oscillator 232input voltage V_(b). A transistor 244 has its source connected toground, its drain connected to node V₃, and its bias connected to nodeV₂. A transistor 246 has its source connected to ground, its drainconnected to oscillator output OUT, and its bias connected to node V₃and the source of M₃.

Given the preceding, NMOS transistor 236 is a first amplifier, with itsgate driven by PMOS transistor 242 drain voltage V₃, and having anoutput at node V₁. NMOS transistor 240 is a second amplifier, with itsgate driven by PMOS transistor 234 drain voltage V₁, and having anoutput at node V₂. NMOS transistor 244 is a third amplifier, with itsgate driven by PMOS transistor 238 drain voltage V₂, and having anoutput at node V₃. Node V₃ drives the gate of transistor 246 so as toprovide the oscillator output shown as OUT, and node V₃ is fed back todrive the gate of NMOS transistor 236 (the first amplifier) asdescribed. Thus, the first, second and third amplifiers are effectivelyconnected in a “ring” structure with the sequential complementaryconnectors creating an oscillating signal.

Generally, in 3-stage ring oscillators, there is a one third phase delaybetween each stage (from V₁ to V₂, from V₂ to V₃, and from V₃ to V₁). Asshown in FIG. 2D, the injection signal V_(inj) is injected (at M₁, M₂and M₃) such that it affects all three stages (V₁, V₂, V₃). (V_(inj),V₁, V₂ and V₃ are also used to refer to respective nodes in the ILFD230.) The ILFD 230 as designed acts as a frequency divider with adivision ratio of three (3). The injection signal V_(inj) thereforecauses the oscillator 232 to lock to a frequency that is one third ofthe frequency of the injection signal V_(inj).

The inventors endeavor to disclose new and advantageous approaches toproducing low-power, low-phase noise periodic oscillator signals (e.g.,electronic device clock signals), as further described below.

SUMMARY

The inventors have discovered new approaches to methods, devices andsystems for low-power, low-phase noise oscillators.

Preferred embodiments include, for example, producing, using anoscillator, a signal having a base frequency component, an Mth harmoniccomponent and a Pth harmonic component, wherein M and P are selectedintegers and M>P>1; filtering said signal through one or more bandpassfilters comprising at least two resonators, said filters having Q factor≥5, said filters configured to pass said Mth and Pth harmoniccomponents; multiplying said filtered Mth and Pth harmonic componentstogether to produce a multiplied signal, and filtering said multipliedsignal using a low pass filter to pass a difference between saidfiltered Mth and Pth harmonic components, said difference comprising afiltered beat frequency waveform; and injecting said filtered beatfrequency waveform into said oscillator to thereby injection lock saidsignal to said filtered beat frequency waveform.

Preferred embodiments also include, for example, a self-injectionlocking clock circuit, including: an oscillator configured to output aperiodic signal with at least a base frequency and configured toinjection lock to an injected signal; one or more bandpass filters withQ factor ≥5, said filters configured to pass an Mth harmonic and a Pthharmonic of said base frequency to output a filtered Mth harmonic and afiltered Pth harmonic, M and P being integers selected in at leastpartial dependence on said base frequency and M>P>1, said filtersoperatively coupled to said oscillator to filter said oscillator output;a multiplier configured to multiply said filtered Mth harmonic by saidfiltered Pth harmonic to produce a multiplied Mth*Pth harmonic waveformhaving a beat frequency component comprising a difference between saidfiltered Mth harmonic and said filtered Pth harmonic; and a low passfilter configured to pass said beat frequency component as a filteredbeat frequency component, such that said filtered beat frequencycomponent is injected into said oscillator.

Numerous other inventive aspects are also disclosed and claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosed inventive scope will be described with reference to theaccompanying drawings, which show important sample embodiments and whichare incorporated in the specification hereof by reference, wherein:

FIG. 1 schematically shows an example of a self-injection lockingoscillator which injection locks to a harmonic of its base frequency toproduce a low-phase noise output signal.

FIG. 2A shows an example of a locking range graph 200 of an oscillator.

FIG. 2B schematically shows an example of a self-injection locking phaselocked loop.

FIG. 2C schematically shows an example of a self-injection-lockingoscillator.

FIG. 2D shows an example of a transistor-level diagram of adivide-by-three injection locked frequency divider.

FIG. 3 schematically shows an example of a self-injection lockingoscillator using an injected harmonic of an oscillator's base frequencyto injection lock the oscillator.

FIG. 4A schematically shows an example of a 3-stage ring oscillator.

FIG. 4B shows an example of a transistor-level diagram of a 3-stage ringoscillator.

FIG. 5 shows an example of a graph of the perturbation projection vector(PPV) induced by an injected signal on an oscillator.

FIG. 6 schematically shows an example of a self-injection lockingoscillator according to a preferred embodiment, which injection locks toa difference between two harmonics of an oscillator base frequency.

FIG. 7A shows an example waveform of a multiplier output produced usingtwo high-Q filters passing different harmonics of the base frequency.

FIG. 7B shows an example Fourier transform of the sum of the outputs offilters passing harmonics of the base frequency according to preferredembodiments.

FIG. 8 schematically shows an example of a self-injection lockingoscillator according to a preferred embodiment, which injection locks toa difference between two harmonics of an oscillator base frequency.

FIG. 9 schematically shows an example of a mixer and filter forselecting the beat frequency from a signal comprising the sum of twodifferent harmonics of the base frequency.

FIG. 10 shows a cross-sectional view of an example of the structure of aBAW resonator.

FIG. 11 schematically shows an example of a transistor-level diagram ofa current controlled oscillator that can be used to implement aself-injection locking oscillator.

FIG. 12 shows an example of the voltage vs. frequency behavior of aself-injection locking oscillator which injection locks to a differencebetween two harmonics of an oscillator base frequency.

FIG. 13A shows an example of a process, according to preferredembodiments, for self-injection locking an oscillator by injecting intothe oscillator a harmonic of a base frequency of the oscillator.

FIG. 13B shows an example of a process, according to preferredembodiments, for self-injection locking an oscillator by injecting intothe oscillator a beat frequency waveform comprising the differencebetween two harmonics of a base frequency of the oscillator.

DETAILED DESCRIPTION OF SAMPLE EMBODIMENTS

The numerous innovative teachings of the present application will bedescribed with particular reference to presently preferred embodimentsby way of example, and not of limitation. The present applicationbroadly describes inventive scope, and none of the statements belowshould be taken as limiting the claims generally.

The present application discloses new approaches to producing low-power,low-phase noise clock signals, particularly using circuits andcomponents that can be incorporated into an integrated circuit (IC)package, preferably on-chip.

Multiple related approaches, which can be combined in potentiallysynergistic ways, are disclosed below in two differently-titledsections. Section titles should not be read as limiting the claims orthe corresponding disclosure, and disclosure in each section should beread in light of the entire disclosure herein. These sections generallyrelate to (1) use of self-injection locking to a harmonic of a basefrequency to produce a low-power, low-phase noise oscillator, and (2)use of self-injection locking to the difference between two harmonics ofa base frequency to produce a low-power, low-phase noise oscillator.

Some exemplary parameters will be given to illustrate the relationsbetween these and other parameters. However it will be understood by aperson of ordinary skill in the art that these values are merelyillustrative, and will be modified by scaling of further devicegenerations, and will be further modified to adapt to differentmaterials or architectures if used.

I. Self-Injection Locking to a Harmonic of an Oscillator Base Frequency

FIG. 1 schematically shows an example of a self-injection lockingoscillator 100 according to a preferred embodiment which injection locksto a harmonic of its base frequency to produce a low-phase noise outputsignal. The oscillator 102 oscillates at a base frequency ω₀, andproduces an oscillator output signal 104. The oscillator 102 generallyalso produces, and the output signal 104 comprises, harmonics(multiples) of the base frequency ω₀. The oscillator 102 is alsoconfigured to receive an input injection signal 106 such that, when theinjection signal is of an appropriate frequency (as explained furtherbelow) and sufficient amplitude, the oscillator 102 locks to theinjection signal 106.

The output signal 104, at base frequency ω₀, can also be mathematicallyrepresented by e^(jθ), which is a general representation for a periodicoscillating signal.

Preferably, the oscillator 102 is selected to be relatively simpleand/or inexpensive and/or small and/or otherwise convenient in design,manufacture and operation (enabled by the power and phase noiseadvantages of self-injection locking to a group-delayed harmonic of theoscillator output signal). A ring oscillator is an example of anoscillator that meets these critera.

If it is inconvenient to use the harmonics generated by the oscillator102 as input to a high-Q filter 108 that in turn drives the oscillator102 (further described below), or if the oscillator 102 does notgenerate harmonics (e.g., it produces a sine wave), then the output 104of the oscillator 102 can be fed into a harmonic generator 110, e.g., asquare wave generator or a narrow pulse generator. “Inconvenient” refersto the output signal 104 generated by the oscillator 102 havinginsufficient amplitude at a desired harmonic of the base frequency ω₀(e.g., the third harmonic, 3ω₀) to reliably enable injection locking.The harmonic generator 110 generates harmonics of frequencies of signalsinput into the harmonic generator 110. The harmonic generator 110 uses aportion of the energy in the oscillator output 104 to generate harmonicsmω₀ of the oscillator's 102 base frequency ω₀. Here, mω₀ refers tomultiples in of the base frequency ω₀. The harmonic generator's output112 includes the Nth harmonic of the base frequency ω₀. The Nth harmoniccan also be mathematically represented by e^(jNθ), which is a generalrepresentation for an Nth harmonic of a periodic oscillating signal.

The harmonic generator's output 112 is fed into a high-Q filter 108. Thehigh-Q filter 108 is a bandpass filter tuned to pass a selected Nthharmonic Nω₀ of the oscillator's 102 base frequency ω₀. For example, the3rd harmonic of ω₀ would be 3ω₀. The high-Q filter 108 passes only theselected Nth harmonic (generally, based on filter quality), reduces thephase noise and amplitude noise in the transmitted signal, andintroduces a group delay. The filtered Nth harmonic signal 106 can alsobe mathematically represented by H(jω)e^(jNθ), which is a generalrepresentation for a transfer function of an Nth harmonic of a periodicoscillating signal.

The high-Q filter 108 is used to bandpass filter the oscillator outputsignal 104 to produce, with a group delay, a low-phase noise filteredsignal 108 at the selected Nth harmonic Nω₀ of the base frequency ω₀.This low-phase noise or “clean”, group-delayed filtered signal 108 atfrequency Nω₀ is injected into the oscillator 102. That is, theoscillator output signal 104 is, after filtering (and optional harmonicgeneration), injected back into the oscillator 102—thus, self-injection.

High Q factor “isolates” the system and makes it resistant to change.Higher Q factor means more energy is required to change the frequencyoutput of the filter 108, and less energy is required to maintain aconstant-frequency filtered signal 108. High Q factor therefore resultsin high filter 108 efficiency and large group delay.

While various types of high-Q filters can be used to implement theoscillator of FIG. 1, the high-Q filter 108 is preferably a MEMS(micro-electromechanical systems) filter such as a filter made using abulk acoustic wave (BAW) resonator. It is particularly advantageous touse an oscillator as shown in FIG. 1 to produce a clock signal in the200 MHz to 1 GHz range. This frequency range is generally too high foruse of a quartz crystal oscillator to produce the clock signal directly,and sufficiently small BAW resonators for use on-chip generally resonateat frequencies significantly greater than 1 GHz (dividing down a, forexample, 2.5 GHz BAW resonator output generally entails relatively highpower consumption). However, as shown in, e.g., FIGS. 1 and 3, high-Q,high frequency MEMS resonators, which can be manufactured compactly andconveniently, and which can be small enough for inclusion on-chip, canbe used to produce a low-power, low-phase noise clock signal.

Once the filtered signal 106 at frequency Nω₀ is injected into theoscillator 102, the oscillator 102 injection locks to the low-phasenoise filtered signal 106. That is, the frequency of the waveform of theoutput signal 104 is repeatedly corrected (phase shifted, as furtherdiscussed with respect to FIG. 5) by the injection signal 106 to producean injection locked output signal 104 with eventual steady statefrequency {circumflex over (ω)}₀. In an N-stage oscillator, for example,this can comprise an injection signal 106 with frequency Nω₀simultaneously correcting N time shifted versions of the oscillatorwaveform, corresponding to the N stages of the oscillator. Because theinjected Nth harmonic frequency Nω₀ is a multiple of the base frequencyω₀, injecting the Nω₀ signal injection locks the oscillator 102 at(approximately, as described below) its base frequency ω₀, which furtherresults in simultaneously injection locking the harmonics mω₀.

There is a (generally small) difference between ω₀ and the steady stateinjection locked frequency {circumflex over (ω)}₀ as a result of thegroup delay caused by the high-Q filter 108. This can be describedmathematically as, e.g., {circumflex over (ω)}₀=Nω₀+Δω₀, where{circumflex over (ω)}₀ is the steady state frequency of the injectionlocked oscillator output 104, and Δω₀ is the group delay-induced changeand is generally small. Because the base frequency ω₀ and the Nthharmonic frequency Nω₀ are coupled (one is a multiple of the other),injection locking using the oscillator's Nth harmonic comprisesinjection locking the oscillator 102 at its base frequency ω₀. Further,the group delay in the self-injected signal 106 results in a low-phasenoise output signal 104 at the oscillator's base frequency ω₀, with aslight change in the base frequency ω₀ as an additional result of thegroup delay. Required power to sustain stable, low-phase noiseoscillation is relatively low because of the relatively low outputfrequency ω₀ of the oscillator 102 compared to the harmonic frequencyNω₀ passed by the filter 108.

Initially, the output signal 104 produced by the oscillator 102 haselevated phase noise, which is significantly reduced as theself-injection locking oscillator 100 stabilizes and the oscillator 102enters a self-injection locked state.

Using a high-Q filter 108 also assists in enabling low-power operationof disclosed embodiments, both because a high-Q filter 108 is itselfefficient, and because phase noise improvement, comparing an output 104from a free running oscillator 102 to an output 104 of a steady stateinjection locked oscillator 102 in a preferred embodiment, isproportional to the amplitude of the injected signal and the Q factor ofthe filter 108. (“Free running” refers to the oscillator 102 prior to orisolated from injected signal perturbation.) Q factor of the filter 108is proportional to increased group delay, and increased Q factor (hence,increased group delay) is proportional to phase noise improvement.

As further detailed later, phase noise improvement in embodiments asdisclosed herein is also proportional to the perturbation projectionvector (see FIG. 5) at the selected Nth harmonic, and to the number N ofthe selected harmonic. Some considerations in choosing N are detailedbelow.

A high-Q (narrow bandwidth) filter 108 is used so that a very“clean”—low-phase noise—signal can be injected into a free running,relatively high-phase noise oscillator 102. E.g., edges of the freerunning oscillator's 102 signal 104 are not exact. The low-phase noisefiltered signal 108 gives the oscillator 102 a relatively precisefrequency to injection lock to, and periodically corrects the edgetiming of the oscillator's signal 104.

The high-Q filter 108 is also used because it introduces a significantgroup delay into the oscillator's signal 104. Self-injection locking byan oscillator 102 to its filtered, group-delayed harmonic significantlyreduces the oscillator signal's 104 phase noise. As an additionalresult, though the oscillator signal 104 is (after some manipulation,e.g., by a harmonic generator 110 and the high-Q filter 108) injectedback into the oscillator 102, the oscillator signal 104 generally doesnot injection lock to precisely the oscillator's 102 own base frequencyω₀. Rather, because of, for example, the introduced group delay, therewill generally be a slight difference in the stable, injection lockedoscillator signal 104 with respect to the original base frequency ω₀.

The low-phase noise Nth harmonic of the base frequency Nω₀, output fromthe high-Q filter 108, is injected back into the oscillator 102. Theoscillator 102 then injection locks to the frequency Nω₀ signal, withsignificantly reduced phase noise in the oscillator output signal 104(e.g., −30 dB) as a result of the injection locking.

Implementing oscillator 102 as an N-stage ring oscillator (for example),and implementing high-Q filter 108 using a BAW resonator (also called a“BAW filter”), will generally require less power (e.g., half as muchpower) to produce a stable low noise clock signal than if the Nω₀frequency BAW resonator were instead used with a 1/N divider to producea clock signal. This advantage is related to the Barkhausen stabilitycriterion: in a linear circuit with a feedback loop, the circuit willsustain steady state oscillations only at frequencies for which the loopgain is equal to unity in absolute magnitude, and the phase shift aroundthe loop is zero or an integer multiple of 2π (360°). The circuit asshown in FIG. 1 decouples unity loop-gain from phase noise performance.

Preferably, in embodiments as shown in FIG. 1, the high-Q filter 108will have a Q factor of at least 5 for the clock circuit to save power(e.g., in comparison to a clock using a BAW resonator as an oscillatorand using a divider to produce a final, lower-frequency output signal).Also, preferably, in embodiments as shown in FIG. 1, the high-Q filterwill have a Q factor of at least 10 for the oscillator circuit to showsignificant phase noise improvement. The present inventors contemplatethat, for lower Q factor, thermal noise and inefficiencies relating tonoisy filter output with minimal group delay may outweigh advantagesfrom self-injection locking.

As shown in FIG. 5 and explained at further length below, the relativelynoisy (until injection locked) harmonic of frequency (approximately) Nω₀of the oscillator's 102 base frequency ω₀ should be close enough to theinjected signal 106 of frequency Nω₀ (as also discussed in theBackground) to phase shift the oscillator signal 104 into an injectionlocked state. Here, “close enough” means that harmonic Nω₀ of the basefrequency ω₀ of the free running oscillator 102 is both: within thelocking range of the oscillator 102; and within the bandwidth of thehigh-Q filter 108—preferably, close to the central frequency of thehigh-Q filter 108—so that the filtered harmonic Nω₀ signal's amplitudeis sufficient (is not so attenuated by the high-Q filter 108) to induceinjection locking in the oscillator 102 (see FIG. 2A). The oscillatorsignal 104, when the oscillator 102 is free running or not yet injectionlocked, has a particular edge timing (though edges are not exact). Theinjected waveform 108 repeatedly (periodically) nudges that timing toinjection lock the oscillator signal 104 waveform.

As discussed below with respect to FIG. 6 (see, e.g., discussion ofpower detector 626) and FIG. 11, feedback and control are preferablyprovided to tune the base frequency ω₀ of the oscillator 102 so that theNth harmonic Nω₀ of the base frequency ω₀ of the free running oscillator102 is “close enough” to the injected signal 106 of frequency Nω₀ toenable injection locking (see explanation of “close enough” above). Theoscillator can be tuned by, for example, changing the bias current in aring oscillator, or by changing the capacitance at the nodes of the ringoscillator (for embodiments in which the oscillator 102 is a ringoscillator). Tuning can generally be stopped once conditions aredetected (by feedback and control) to be adequate for injection locking,at which point injection locking will tend to adjust the base frequencyω₀ of the oscillator 102 so that the Nth harmonic Nω₀ of the basefrequency ω₀ closely matches the central frequency of the high-Q filter108.

Phase noise improvement of the stable, injection locked output 104 (overthe free running output 104) of embodiments as shown in FIG. 1 isproportional to the number N of the selected Nth harmonic (with a small,group delay-induced difference). That is, generally, the higher theharmonic, the lower the phase noise of the output 104. The harmonicnumber N can also be selected based on, for example, the desired circuitsize (BAW resonators, for example, are smaller the higher the frequencyat which they resonate); the desired complexity of the oscillator 102,since oscillator 102 circuit design suitable to receive signal injectionis generally more complex the higher the harmonic to be injected; andthe amount of tolerated device noise contribution, as device noise canbe more significant at higher harmonics—higher harmonics generally havelower amplitudes, increasing the proportional significance of devicenoise. Odd N is preferred, because square waves contain primarily (idealsquare waves contain only) components of odd-integer harmonics of thebase frequency ω₀. However, embodiments using even harmonics are alsocontemplated, e.g., injection into an LC oscillator at the 2nd or 4thharmonic of the LC oscillator's base frequency.

A self-injection locking oscillator as shown in FIG. 1, which can beused to implement, e.g., a clock circuit in an integrated circuitdevice, can be implemented within a device area of, for example, 200μm×200 μm. A self-injection locking clock as shown in FIG. 1 can befully integrated into the same chip package, or (in some embodiments)into the same substrate, as the device driven by the output clocksignal.

FIG. 3 schematically shows an example of a self-injection lockingoscillator 300 using an injected harmonic Nω₀ of an oscillator 302 basefrequency ω₀ to self-injection lock the oscillator 302. A pulsegenerator 304 (which is essentially a harmonic generator 110 of FIG. 1),producing a signal 306 with components at the oscillator's 302 basefrequency ω₀ (e.g., 840 MHz) and at harmonics mω₀ (for a wide range ofm≥2) of the oscillator's 302 base frequency ω₀, is connected to a high-Qfilter 308 (e.g., a 2.52 GHz BAW filter with Q=1000) configured toprimarily pass a selected Nth harmonic 310 of the oscillator's 302 basefrequency ω₀ (in this example, the 3rd harmonic). The oscillator 302 canbe, for example, a ring oscillator (further discussion of FIG. 3assumes, for purposes of example, that the oscillator 302 is a ringoscillator). Though the high-Q filter 308 blocks most of the pulsegenerator signal 306 except at the selected filter frequency—i.e.,blocks the base frequency ω₀ and most of the harmonics mω₀ (with theexception of the Nth harmonic Nω₀), to an extent generally determined bythe Q factor of the high-Q filter 308—power loss can be held relativelylow if a relatively low base frequency ω₀ is used (e.g., ≤1 GHz).

The output 310 of the high-Q filter 308 is injected into the oscillator302, e.g., a ring oscillator. Though the filter output 310 willgenerally be a relatively low-amplitude signal, an appropriatelydesigned ring oscillator will generally be able to injection lock tothat low-amplitude signal. One of ordinary skill in the arts ofintegrated circuit oscillator circuit design will understand how toconfigure a ring oscillator (or other types of oscillator) for thispurpose, and an example circuit design is shown in FIG. 4B. The output312 of the ring oscillator 302 is fed back into the pulse generator 304,and also comprises the output of the oscillator circuit.

The structure of the oscillator 302 generally determines which harmonicwill induce injection locking in the oscillator 302, assuming theinjected harmonic is within the corresponding locking range. Forexample, an N-stage ring oscillator (see FIG. 4A) will generally lock toits base frequency as a result of injecting the Nth harmonic of the basefrequency into all N stages. Injection locking the N-stage ringoscillator to its base frequency will simultaneously injection lock thering oscillator's harmonics (if any) as well. For example, if N is 3,then a 3-stage ring oscillator will injection lock on injection of its3rd harmonic into all three stages (with a slight difference between thefree running base frequency ω₀ and the steady state injection lockedbase frequency {circumflex over (ω)}₀ induced by the group delay causedby the high-Q filter 308).

FIG. 4A schematically shows an example of a 3-stage ring oscillator 400.A 3-stage ring oscillator 400 can comprise, as shown, three inverters402 connected in series, with the output of the third inverter 402 fedback into the input of the first.

FIG. 4B shows an example of a transistor-level diagram of a 3-stage ringoscillator configured to receive an injected signal into each of itsthree stages. As shown, the design of FIG. 4B implements an embodimentof a ring oscillator usable as oscillator 102 (see FIG. 1) or oscillator302 (see FIG. 3), as would be readily designed by someone of ordinaryskill in the art of integrated circuit oscillator circuit design.

FIG. 5 shows an example of a graph of the perturbation projection vector(PPV) induced by an injected signal on an oscillator. The PPV shows howthe oscillator signal changes if a specific signal is injected at aspecific time during its period (PPV is periodic with the same period asthe oscillator). That is, the PPV shows how much the oscillator signal'sphase changes—i.e., advances or delays—based on the timing and amplitudeof the injected signal. In the system represented by FIG. 5, theoscillator has a three times longer period than the injected signal(approximately 1.2 ns, versus approximately 0.4 ns).

If a delta function (a pulse) is injected where the derivative of theoscillator signal's voltage with respect to time (the slope of theoscillator waveform) is not zero, the phase of the oscillator's signalwill be phase shifted. Conversely, if a delta function is injected wherethe derivative of the oscillator signal's voltage with respect to timeis zero, the phase of the oscillator's signal will not be phase shiftedby the injected delta function.

The median voltage (v) value of the PPV as shown in FIG. 5 representsthe zero value of the system, the voltage value around which the systemoscillates. At the median voltage value of the PPV as shown in FIG. 5,the phase of the oscillator signal is not shifted by the injectedsignal. As shown in FIG. 5, PPVs are time dependent, that is, injectionat different time points in an oscillator signal's period causesdifferent shifts in phase of the oscillator's signal. Also, PPVs areperiodic; for an injection signal with frequency Nω₀, a PPV willgenerally have frequency Nω₀, and will cause the oscillator to injectionlock to the Nth harmonic.

If a signal injected into the oscillator results in the integral of theperturbation projection vector multiplied by the injection signal(voltage/time) equaling zero, the oscillator is not affected by theinjection signal. This also corresponds to the oscillator beinginjection locked to the injection signal, with the oscillator and theinjection signal being in phase with each other. If the integral of thePPV multiplied by the injection signal equals a constant value, then theoscillator is injection locked to the injection signal with a specificand fixed phase difference. If the integral of the PPV multiplied by theinjection signal equals a linear function of time t (e.g., Δω₀t), thenthe oscillator will lock to the injection signal with a frequencydifference Δω₀. Generally, other results—other values of the integral ofthe PPV multiplied by the injection signal—will correspond to theinjection signal perturbing the oscillator. In this latter case,depending on, e.g., the structure of the oscillator and where in theoscillator the signal is injected, the injection signal will typicallyperturb the oscillator in a way that will nudge it closer to injectionlocking with a zero or other constant value for the PPV multiplied bythe injection signal.

Injection locking is achieved when the frequency and phase of theoscillator are such that the integral of the product of the PPV and theinjection signal equals zero, a constant or a linear function of time t.If the oscillator phase deviates from its injection locked state, suchthat the integral of the PPV multiplied by the injection signal nolonger equals one of these types of values, the injection signal willagain perturb the oscillator phase to cause it to return to an injectionlocked state. Injection locking can be thought of as being caused bynegative feedback inherent in the structure of the oscillator receivingan injected signal. For this reason, injection locking to a “clean”signal reduces the phase noise of the oscillator.

As disclosed herein, the inventors have discovered methods and systemsfor producing a low-power, low-phase noise periodic oscillating signalusing a self-injection locking oscillator. For example, an N-stageoscillator can be configured to receive an injected signal into each ofthe oscillator's N stages and connected in looped series with,optionally, a harmonic generator, and a high-Q filter. The high-Qfilter, preferably comprising a compact MEMS resonator, passes an Nthharmonic of the base frequency of the oscillator with a group delay. Thegroup-delayed Nth harmonic of the oscillator's base frequency isself-injected into the oscillator—that is, the oscillator's modifiedoutput is injected back into the oscillator. The oscillator output isinjection locked by the injected Nth harmonic to the oscillator's basefrequency. The oscillator's base frequency consequently injection locksto itself, with a slight change resulting from the group delay. Thissignificantly reduces phase noise in the injection locked oscillatoroutput signal (e.g., −30 dB).

II. Self-Infection Locking to a Difference Between Two Harmonics of anOscillator Base Frequency

FIG. 6 schematically shows an example of a self-injection lockingoscillator 600 according to a preferred embodiment, which injectionlocks to a difference between two harmonics of an oscillator 602 basefrequency ω₀. The oscillator 602 oscillates at a base frequency ω₀, andproduces an oscillator output signal 604. The oscillator 602 generallyalso produces, and the output signal 604 comprises, harmonics(multiples) mω₀ of the base frequency ω₀. The oscillator 602 is alsoconfigured to receive an input injection signal 606 such that, when theinjection signal is of an appropriate frequency (as explained furtherbelow) and sufficient amplitude, the oscillator 602 locks to theinjection signal 606. Once the oscillator 602 reaches steady stateinjection locked oscillation, the base frequency of the oscillator 602is referred to as {circumflex over (ω)}₀.

The oscillator output 604 is optionally fed into a pulse generator 608,which can be configured as a harmonic generator, and/or as an energysource for driving the self-injection locking oscillator 600. In anenergy source role, the pulse generator 608 can assist in maintainingunity loop gain in the oscillator circuit, further to the Barkhausenstability criterion. The pulse generator 608 produces a signal 610 withcomponents at the oscillator's 602 base frequency ω₀ and at harmonicsmω₀ (for a wide range of in ≥2) of the oscillator's 602 base frequencyω₀. The purpose and function of a harmonic generator in a self-injectionlocking oscillator is further discussed with respect to FIG. 1 (harmonicgenerator 110) and FIG. 3 (pulse generator 304).

The output 610 of the pulse generator 608 is filtered by two closelymatched high-Q filters 612, 614, which are bandpass filters each tunedto pass a respective, different selected M and P harmonic, withfrequencies Mω₀ and Pω₀, of the oscillator's 102 base frequency ω₀.

As further discussed with respect to FIG. 10, “closely matched” meansthat the two filters 612, 614 are designed so that their responses toabsolute drifts in their passed frequencies are substantiallyidentical—preferably, identical within design and manufacturing limits.Absolute drifts are fixed-value changes in passed frequencies of afilter, i.e., changes that are not proportional to the passed frequencyof the filter. Absolute drifts can be caused by, for example: aging ofthe device, such as due to repeated thermal and/or vibration-inducedstress; device packaging stress; and random variations in devicemanufacturing process, such as overlay or critical dimension errors thatare insufficient to cause device failure. These phenomena can also causerelative shift, i.e., proportional changes in passed frequencies of afilter.

It is advantageous, in design and manufacture of closely matched high-Qfilters 612, 614, for the filters 612, 614 to be located in proximity toeach other on the same device, e.g., integrated circuit. Fabricating thefilters 612, 614 in proximity to each other on the same chip willgenerally result in the filters 612, 614 receiving substantially thesame stresses—individually and cumulatively, during fabrication andduring operation—at substantially the same times. If the filters 612,614 are closely matched, then the filters 612, 614 receiving the samestresses will result in them experiencing the same absolute drifts.Because the oscillator 602 injection locks to the difference between theharmonics Mω₀ and Pω₀, or to a harmonic (a multiple) of that difference(as further explained below), absolute drifts applied to both filterseffectively cancel out. That is, for absolute drifts ΔMω₀ and ΔPω₀,where ΔMω₀=ΔPω₀, the cancelling out is as shown in the following Eq. 1:(Mω ₀ +ΔMω ₀)−(Pω ₀ +ΔPω ₀)=(Mω ₀ +ΔMω ₀)−(Pω ₀ +ΔMω ₀)=Mω ₀ −Pω ₀  Eq.1:

While various types of high-Q filter can be used to implement theoscillator of FIG. 6, the high-Q filters 612, 614 are preferably MEMSfilters, such as filters made using BAW resonators. BAW resonators areparticularly advantageous because, for example, they can be fabricatedin very close proximity to each other (e.g., on the same chip).Fabrication on the same chip enables BAW resonators to closely match,generally significantly more so than filters fabricated on differentchips or in different fabrication lots.

It is particularly advantageous to use an oscillator circuit as shown inFIG. 6 to produce a clock signal in the 100 MHz to 1 GHz range.Advantages in using filters comprising MEMS resonators are discussedherein with respect to, e.g., FIG. 1 and high-Q filter 108, as well asFIG. 10. As shown in, e.g., FIGS. 6 and 8, high-Q, high frequency MEMSresonators, which can be manufactured compactly and conveniently, andwhich can be small enough for inclusion on-chip, can be used to producea low-power, low-phase noise clock signal.

The high-Q filters 612, 614 operate as discussed with respect to FIG. 1and high-Q filter 108, producing “clean”, group-delayed signals. High-Qfilter 612 produces an output 616 with a frequency comprising the Mthharmonic Mω₀ of base frequency ω₀, and high-Q filter 614 produces anoutput 618 with a frequency comprising the Pth harmonic Pω₀ of basefrequency ω₀. The two high-Q filter output signals 616, 618 can also berepresented mathematically as a function of time t as cos(Mω₀t) andcos(Pω₀t).

The high-Q filter outputs 616, 618 are multiplied together by amultiplier 620, to produce multiplier output 622. (This operation isroutinely performed in communications systems by mixers; see below withrespect to FIG. 9 for an example and further explanation.) Themultiplier output 622 can be expressed mathematically as:cos(Mω ₀ t)cos(Pω ₀ t)=½[cos(Mω ₀ −Pω ₀)t+cos(Mω ₀ +Pω ₀)t]  Eq. 2:

In Eq. 2, the cos(Mω₀−Pω₀)t term of the multiplier output 622 is thebeat frequency of the two filter outputs 616, 618, i.e., the differencebetween the two frequencies. As mentioned above and further explainedwith respect to FIG. 10, injecting the beat frequency (the difference)into the oscillator 602 to cause the oscillator 602 to injection lockmeans that the high-Q filters 612, 614 can be designed to reduce oreliminate undesired frequency variations in the injection signal 606caused by absolute drift and thermal drift.

FIG. 7A shows an example waveform 700 of a multiplier output 622produced using two high-Q filters 612, 614 passing different harmonicsMω₀ and Pω₀ of the base frequency ω₀. As shown in FIG. 7A, a relativelyhigh frequency oscillation 702 is contained within a lower frequencyamplitude envelope 704 (with aberrations 706 due, e.g., to harmonicspassed by the filters 612, 614 other than the selected M and P harmonicsas a result of the filters 612, 614 having finite Q factors). The higherfrequency oscillation 702 corresponds to the cos(Mω₀+Pω₀)t term of themultiplier output, and the lower frequency amplitude envelope 704corresponds to the cos(Mω₀−Pω₀)t term of the multiplier output 622. Thecos(Mω₀−Pω₀)t term will also describe the injection signal 606 that willbe injected (self-injected) into the oscillator 602, and corresponds toeither the base frequency ω₀, or to an Nth harmonic Nω₀ of the basefrequency ω₀, as explained below.

FIG. 7B shows an example Fourier transform 708 of the sum of the outputsof filters passing harmonics of the base frequency according topreferred embodiments. In the example shown in FIG. 7B, the basefrequency ω₀=100 MHz component 710 of the filter outputs 716, 718 isrelatively small; first filter 612 primarily passes first frequency 712Mω₀=2.5 GHz (the 25th harmonic), and second filter 614 primarily passessecond frequency 714 Pω₀=2.4 GHz (the 24th harmonic). The aberrations706 from the amplitude envelope 704 discussed with respect to FIG. 7Aare due to unwanted harmonics 716 passed by the filters 612, 614. Whilesuch high-numbered harmonics will generally have relatively lowamplitude, the difference between them (the beat frequency waveform)will generally have an envelope with a higher amplitude than the outputof either of the BAW resonators alone.

Returning to FIG. 6, a low pass filter 624 is used to filter out thecos(Mω₀+Pω₀)t term, with its relatively high frequency, from themultiplier output 622. The remaining signal 606, which can berepresented as cos(Mω₀−Pω₀)t—the beat frequency of the two high-Q filteroutputs 616, 618—is injected into the oscillator 602.

The oscillator 602 is preferably tuned so that ω₀ or Nω₀ equals the beatfrequency of the high-Q filters 612, 614. This tuning is performed usingfeedback provided by a power detector 626 to cause the oscillator 602 tooutput a base frequency ω₀ that results in an injection locked outputsignal 604 of sufficient amplitude (e.g., maximal amplitude). Theoscillator 602 is tuned by, for example, selecting orvoltage-controlling capacitors controlling the oscillator 602 basefrequency; preferably, the base frequency ω₀ can be both increased anddecreased (e.g., depending on control inputs provided to capacitors).This feedback and tuning are used to address circuit variability basedon process variation, temperature, idiosyncrasies of the power supply,and other factors which can affect the waveform frequency and envelopeamplitude by, for example, 30% (or more). Tuning the oscillator 602 isfurther described with respect to FIG. 11.

If the beat frequency of the two high-Q filter outputs 616, 618 is nearthe base frequency ω₀ of the free running oscillator 602 (i.e., closerto the base frequency ω₀ than to harmonics mω₀ of the base frequency ω₀)then the oscillator 602 will injection lock to its base frequency ω₀.(As previously explained, self-injection locking to a group-delayedsignal will actually cause the oscillator 602 to injection lock to someslightly different frequency {circumflex over (ω)}₀=ω₀+Δω₀.) This casecan be approximated as Mω₀−Pω₀=ω₀. That is, M−P=1, meaning that the Mthand Pth harmonics filtered by the high-Q filters 612, 614 are adjacentharmonics of the base frequency ω₀.

Alternatively, if the beat frequency of the two high-Q filter outputs616, 618 is near an Nth harmonic Nω₀ of the base frequency ω₀, then (asdiscussed with respect to, e.g., FIGS. 1 and 3) the oscillator 602 willlock as a result of injection of an Nth harmonic Nω₀. This case can beapproximated as Mω₀−Pω₀=Nω₀. That is, M−P=N, meaning that the differencebetween the Mth and Pth harmonics filtered by the high-Q filters 612,614 is the Nth harmonic Nω₀ of the base frequency ω₀. This demonstratesthe synergy between titled Sections I and II of this disclosure: theability to injection lock the oscillator 602 as a result of injection ofits base frequency ω₀ or of a harmonic of its base frequency Nω₀, andthe ability to select the harmonics M and P to which the high-Q filters612, 614 are tuned, provide a wide range of customizability in thecomponent, power, and frequency requirements and performance of aself-injection locking oscillator 600 as shown in FIG. 6.

FIG. 8 schematically shows an example of a self-injection lockingoscillator 800 according to a preferred embodiment, which injectionlocks to a difference between two harmonics of an oscillator 802 basefrequency ω₀. The oscillator 802 can be, for example, an on-chip ringoscillator (e.g., with ω₀=100 MHz), with an output 804 and an input 806by which a signal can be injected into the oscillator 802 to cause theoscillator 802 to injection lock. An optional pulse generator 808generates harmonics mω₀ of the oscillator output 804 using a portion ofthe energy in the oscillator output 804 (that is, the pulse generator808 outputs the base frequency ω₀ and harmonics mω₀ of the basefrequency).

The pulse generator output 810 is filtered through a high-Q filter 812comprising two closely matched high-Q resonators tuned to M and Pharmonics and placed to produce a filter output 814 that will enable awaveform at the beat frequency of the two high-Q resonators (Mω₀−Pω₀) tobe created; preferably, the high-Q resonators are located to facilitategeneration of the sum of their outputs. This can, for example, compriseplacing the high-Q resonators in series and forcing a current throughthem, which will generally result in a voltage that is the sum of theresponses of the two high-Q resonators.

The high-Q resonators are preferably MEMS resonators, and morepreferably BAW resonators for reasons described with respect to, e.g.,FIG. 1. The filter output 814, which is the pulse current multiplied bythe filter impedance, can be mathematically described for a filtercomprising resonators in sequence as: cos(Mω₀t)+cos(Pω₀t).

The filter output 814 is then fed into a mixer and filter 816, whichsquares the filter output 814 and applies a low pass filter to produce awaveform corresponding to the lower frequency component described abovewith respect to FIG. 6, cos(Mω₀−Pω₀)t, i.e., the beat frequency of theoutputs of the two resonators used to make the filter 812. The designand behavior of the mixer and filter 816 is further explained below withrespect to FIG. 9. (“Mixer” is used here to describe a non-linearelement, such as a MOS transistor, that has quadratic non-linearity.)

The group-delayed beat frequency waveform is then self-injected backinto oscillator 802 to cause the oscillator 802 to either injection lockthe base frequency to the beat frequency, producing a steady stateoscillator output 804 base frequency {circumflex over (ω)}₀=ω₀+Δω₀; orto injection lock a harmonic of the base frequency to the beatfrequency, producing a steady state oscillator output 804 with an Nthharmonic such that N{circumflex over (ω)}₀=Nω₀+Δ{circumflex over (ω)}₀;wherein {circumflex over (ω)}₀ is the steady state injection lockedoscillator 802 base frequency, and ω₀ is the free running oscillator 802base frequency.

FIG. 9 schematically shows an example of a mixer and filter 900 forselecting the beat frequency from a signal comprising the sum of twodifferent harmonics of the base frequency. As shown in FIG. 9, a MOSFETtransistor can be used as a mixer 902, and a biasing circuit 904provides the bias voltage for the mixer 902. The mixer 902 squares theinput signal (e.g., pursuant to the transfer function of a MOSFEToperating in saturation), i.e., the filter output 814, which isV_(in)=cos(Mω₀t)+cos(Pω₀t). The waveform of the square of this inputsignal V_(in) can be mathematically represented as:(cos(Mω ₀ t)+cos(Pω ₀ t))²=cos²(Mω ₀ t)+cos²(Pω ₀ t)+2 cos(Mω ₀ t)cos(Pω₀ t)  Eq. 3:

In light of Eq. 2, and given the identity cos² θ=½(1+cos 2θ), the righthand side of Eq. 3 can be rewritten as:½(2+cos(2Mω ₀ t)+cos(2Pω ₀ t))+cos(Mω ₀ −Pω ₀)t+cos(Mω ₀ +Pω ₀)t  Eq. 4:

The terms in Eq. 4 other than the beat frequency waveform, i.e.,cos(Mω₀−Pω₀)t, are of significantly higher frequency than the beatfrequency, and are preferably filtered out using a low pass filter 906such as an R-C filter. The resulting filtered beat frequencywaveform−cos(Mω₀−Pω₀)t−comprising a “clean” (low-phase noise),group-delayed signal at the beat frequency Mω₀−Pω₀ of the two closelymatched high-Q resonators, is preferably used as the injection signal806 for the oscillator 802 (or the oscillator 602).

FIG. 10 shows a cross-sectional view of an example of the structure of aBAW resonator 1000. It is particularly advantageous to use BAWresonators to make high-Q filters 612, 614 or high-Q filter 812, becauseBAW resonators configured to resonate at different harmonics of anoscillator base frequency can be closely matched to respond similarly(or the same) to temperature drift and to absolute drift.

In embodiments as shown in FIG. 10, a BAW resonator 1000 comprises topBragg mirrors 1002 and bottom Bragg mirrors 1004 (acoustic mirrors),which are made of alternating layers of acoustically transparentmaterials with different properties of acoustic impedance, for example,TiW and SiO₂. Between the Bragg mirrors 1002, 1004 is a piezoelectriclayer 1006 (e.g., AlN). A first contact 1008 is electrically connectedto a top electrode 1010 and a second contact 1012 is electricallyconnected to a bottom electrode 1014; electrodes can be made of, e.g.,molybdenum. Excitation of the top and bottom electrodes 1010, 1014induces a voltage across the piezoelectric layer 1006 which causes thepiezoelectric layer 1006 to oscillate, primarily within an active area1016 in which mechanical energy is confined and isolated. The frequencyof oscillation of the piezoelectric layer 1006 is inversely proportionalto the piezoelectric layer's 1006 thickness. The frequency ofoscillation of the piezoelectric layer 1006 is affected by temperature;as further discussed below, the piezoelectric layer's 1006 oscillatingfrequency's temperature response is related to a ratio between thepiezoelectric layer's 1006 thickness and the thickness of a temperaturecompensating oxide 1018 (which passively compensates fortemperature-induced shifts in the frequency of the piezoelectric layer1006) which is disposed between the piezoelectric layer 1006 and the topBragg mirrors 1002. A BAW resonator can be fabricated on a Si substrate1020. A BAW resonator also preferably comprises a protective overcoat1022, e.g., SiN.

In a BAW resonator, frequency change Δω with temperature T can bedescribed as Δω(T)=(1+αT)ω, where α is the temperature coefficient offrequency factor (TCF), which depends on, for example, Young's modulus(stiffness), density change with temperature, and the amount ofvibrational energy stored in the material under consideration within theBAW resonator structure. For BAW resonators tuned to resonate atharmonics Mω₀ and Pω₀ of the base frequency ω₀, temperature response ofthe BAW resonators is described by Δω_(M)(T)=(1+α_(M)T)Mω₀ andΔωP(T)=(1+α_(P)T)Pω₀. This means that, where Mω₀−Pω₀=ω₀, the beatfrequency temperature response is:Δω_(M)(T)−Δω_(P)(T)=(1+α_(M) T)Mω ₀−(1+α_(P) T)Pω ₀=ω₀+α_(M) TMω ₀−α_(P)TPω ₀  Eq. 5:

If α_(M)=α_(P), then beat frequency temperature response equals(1+αT)ω₀.

However, by adjusting the thickness of the temperature compensatingoxide, the α scalar values can be calibrated to eliminate thetemperature coefficient of the beat frequency (in practice, nearlyeliminate, as shown by the empirical example provided below). This willoccur if the temperature-dependent terms in Eq. 5 are set equal:α_(M)TMω₀=α_(P)TPω₀. This is true if

$\frac{\alpha\; M}{\alpha\; P} = {\frac{P}{M}.}$If the BAW resonators are designed such that this condition is true,then the beat frequency temperature response is:

$\begin{matrix}{{{\Delta\;{\omega_{M}(T)}} - {\Delta\;{\omega_{P}(T)}}} = {{\omega_{0} + {\frac{P}{M}\alpha_{P}{TM}\;\omega_{0}} - {\alpha_{P}{TP}\;\omega_{0}}} = \omega_{0}}} & {{Eq}.\mspace{11mu} 6}\end{matrix}$

That is, the temperature-dependent terms cancel out, and beat frequencytemperature response becomes a constant that is nottemperature-dependent: ω₀, the beat frequency, which equals the basefrequency. Note that if Mω₀−Pω₀=Nω₀, then the temperature-dependentterms cancel out to leave the beat frequency, which equals the Nthharmonic of the base frequency.

Controlling TCF to cancel out temperature dependency of the BAWresonators in the high-Q filters 612, 614 or high-Q filter 812 canresult in a significant improvement in temperature-independence of theself-injection oscillator 600 or 800. For example, from TCF=3,400 ppm/°C. to 148 ppm/° C., a 23-fold improvement.

As discussed with respect to FIG. 6, BAW resonators are “closelymatched” if their responses to absolute drifts in their passedfrequencies are substantially identical. Where the base frequency of anoscillator 602 or 802 depends on the beat frequency of a closely matchedpair of high-Q BAW resonators, this means that absolute drifts of theresonators cancel out, resulting in the oscillator 602 or 802 having ahighly stable injection locked base frequency that is substantiallyinvariant with respect to sources of absolute drift. Closely matched BAWresonators can be fabricated by, for example, placing them in proximitywith each other, so that they receive similar stresses, and by changingtheir designs with respect to each other as little as possible toachieve the different frequencies (harmonics M and P) required by theoscillator 600 or 800 to produce the beat frequency used to injectionlock the oscillator 600 or 800. For example, the thickness of the topelectrode layer 1010 or of the piezoelectric layer 1006 can be modifiedto tune a BAW resonator 1000 (generally, the piezoelectric layer 1006will need to be modified to tune a BAW resonator 1000 between harmonicsof an oscillator's 600 or 800 base frequency), or mass loading can beperformed by adding an extra layer of metal or of oxide (which willgenerally result in damping oscillation). Preferably, BAW resonators arefabricated side-by-side on the same chip, with all layers beingidentical except a single layer (other than the temperature compensatingoxide 1018, which is adjusted as disclosed above to cancel outtemperature effects on the beat frequency); the smaller the mismatch,the better, for the purpose of compensating for absolute drift effects.

FIG. 11 schematically shows an example of a transistor-level diagram ofa current controlled oscillator 1100 that can be used to implement aself-injection locking oscillator. As shown in FIG. 11, an oscillator(e.g., oscillator 602 or 802) can be, for example, a 3-stage currentstarved ring oscillator comprising three inverters 1102 and threevoltage-controlled capacitors 1104. In a current starved ringoscillator, lower current results in lower oscillator frequency, andhigher current results in higher oscillator frequency. The function ofthe capacitors 1104 can be adjusted depending on feedback from a powerdetector 622, 818, and can thus be used to tune the base frequency ofthe oscillator 1100. As one of ordinary skill in the art of integratedcircuit oscillator circuit design will understand, other types ofoscillators in which frequency is tunable based on an input signal canalso be used to implement, e.g., embodiments as shown in FIGS. 6 and 8.

FIG. 12 shows an example of the voltage vs. frequency behavior 1200 of aself-injection locking oscillator 600, 800 which injection locks to adifference between two harmonics of an oscillator 602 base frequency ω₀.The plot as shown in FIG. 12 was produced using BAW resonators withresonant frequencies of 2.5 GHz and 2.4 GHz and a voltage controlledring oscillator. At relatively low control voltage 1202 (between about452.2 mV and 467.2 mV), the base frequency of about 96-97 MHz injectionlocks to its 25th and 26th harmonics (2400-2425 MHz and 2496-2522 MHz).At higher control voltage 1204 (between about 467.6 mV and 480.6 mV),the oscillator injection locks at a somewhat stabler 100.4-101 MHz toits 24th and 25th harmonics (2409.6-2424 MHz and 2510-2525 MHz). Aspreviously discussed with respect to, e.g., FIG. 6, the oscillatorinjection locks to a frequency {circumflex over (ω)}₀=ω₀+Δω that isslightly different from the input signal, i.e., the beat frequency ofthe two BAW resonators.

FIG. 13A shows an example of a process 1300, according to preferredembodiments, for self-injection locking an oscillator by injecting intothe oscillator a harmonic of a base frequency of the oscillator. Asshown in FIG. 13A, a periodic signal with base frequency ω₀ is generatedusing an oscillator in step 1302. Optionally, as described with respectto FIGS. 1 and 3, a harmonic generator can be used to generate the Nthharmonic Nω₀ of the base frequency ω₀ using the signal (generated instep 1302) in step 1304. The Nth harmonic Nω₀ is filtered using a high-Qfilter to produce a low phase noise, low amplitude noise, group-delayedsignal with frequency Nω₀ in step 1306. The filtered signal withfrequency Nω₀ is then injected (self-injected) into the oscillator tothereby self-injection lock the oscillator in step 1308.

FIG. 13B shows an example of a process 1310, according to preferredembodiments, for self-injection locking an oscillator by injecting intothe oscillator a beat frequency waveform comprising the differencebetween two harmonics of a base frequency of the oscillator. As shown inFIG. 13B, a periodic signal with base frequency ω₀ is generated using anoscillator in step 1312. Optionally, as described with respect to FIGS.6 and 8 (see also FIGS. 1 and 3), a harmonic generator can be used togenerate the Mth harmonic Mω₀ and the Pth harmonic Pω₀ using the signal(generated in step 1312) in step 1314. The Mth and Pth harmonics arefiltered using at least one high-Q filter, comprising two resonances(e.g., one filter with two resonances, or two filters with one filtereach) in step 1316. The Mth and Pth harmonics Mω₀ and Pω₀ are multipliedtogether, and the multiplied signal is low pass filtered to produce abeat frequency waveform of the two harmonics, with frequency Mω₀−Pω₀, instep 1318. The beat frequency waveform is injected into the oscillatorto thereby self-injection lock the oscillator to base frequency ω₀ instep 1320.

The disclosed innovations (including in Section I and Section II above),in various embodiments, provide one or more of at least the followingadvantages. However, not all of these advantages result from every oneof the innovations disclosed, and this list of advantages does not limitthe variously claimed inventive scope.

-   -   Enables low-power, low-phase noise clock;    -   enables clock resilient against absolute drift;    -   enables elimination of temperature drift in clock output        frequency;    -   enables compact implementation that can be incorporated into an        integrated circuit package and/or be fabricated on-chip;    -   incorporates high frequency high-Q filter(s) without requiring        high base frequency (e.g., significantly more than 1 GHz)        oscillation to be maintained;    -   does not require a divider, but can improve phase noise        proportional to a ratio N between oscillator's base frequency        ω₀, and a selected harmonic Nω₀ of the base frequency;    -   enables fast start-up and stabilization of low-power, low-phase        noise clock;    -   decouples unity loop-gain from phase noise performance;    -   enables use of high frequency, high-Q, compact MEMS resonators        as filters; and    -   enables clock circuit power consumption to be balanced against        clock signal phase noise without affecting oscillator amplitude        or frequency.

As disclosed herein, the inventors have discovered methods and systemsfor producing a low-power, low-phase noise periodic oscillating signalusing a self-injection locking oscillator. For example, an oscillatorcan be configured to receive an injected signal and connected in loopedseries with a harmonic generator (optionally), two closely matchedhigh-Q bandpass filters, a multiplier, and a low pass filter. The high-Qfilters, preferably comprising compact MEMS resonators, pass Mth and Pthharmonics of the base frequency of the oscillator with a group delay.These signals are multiplied together and then fed into a low passfilter to produce a signal corresponding to the beat frequency of—i.e.,the difference between—the Mth and Pth harmonics. The group-delayed beatfrequency waveform is self-injected into the oscillator—that is, theoscillator's modified output is injected back into the oscillator. Theoscillator (the base frequency or a harmonic) locks to the injected beatfrequency. The oscillator's base frequency consequently injection locksto itself, with a slight change resulting from the group delay. Thissignificantly reduces phase noise in the injection locked oscillatoroutput signal (e.g., −32 dB). Also, because the closely matched high-Qfilters respond identically to absolute drifts and the oscillatorinjection locks to the difference between filter output frequencies,absolute drifts are subtracted out. Further, the high-Q filters can bedesigned and fabricated to compensate for each other's temperaturedrifts. As a result, the injection locked oscillator's output is notonly low phase noise, it is also highly resilient against various typesof time- and condition-dependent drift.

MODIFICATIONS AND VARIATIONS

As will be understood by those skilled in the art, the innovativeconcepts described in the present application can be modified and variedover a tremendous range of applications, and accordingly the scope ofpatented subject matter is not limited by any of the specific exemplaryteachings given. It is intended to embrace all such alternatives,modifications and variations that fall within the spirit and broad scopeof the appended claims.

In some embodiments, a base frequency of an oscillator is less than 200MHz or greater than 1 GHz.

In some embodiments, a base frequency of an oscillator can be changedbased on input from outside the oscillator circuit and/or outside adevice comprising the oscillator circuit. In some embodiments, a basefrequency of an oscillator can be changed based on input from within adevice comprising the oscillator circuit.

In some embodiments, different filters configured to pass differentharmonics of an oscillator's base frequency are available to anoscillator circuit, and which of said filters is used to provide afiltered, group-delayed Nth harmonic (or Mth and Pth harmonics) dependson input from outside the oscillator circuit.

In some embodiments, multi-stage oscillators other than ring oscillatorscan be used. In some embodiments, single-stage oscillators can be used.

In some embodiments, a ring oscillator with an even number of stages canbe used, e.g., a fully-differential ring oscillator.

In some embodiments, output frequency ω₀ is selectable, e.g., byselecting which harmonic of the oscillator will be locked. In someembodiments, selecting which harmonic of the oscillator will be lockedcomprises selecting from multiple different oscillator circuits (e.g.,multiple different ring oscillator circuits with different numbers ofstages) that are available (e.g., available on-die). In someembodiments, the harmonic to be locked to can be selected by a user. Insome embodiments, selecting the harmonic to be locked to determines thefinal base frequency ω₀.

In some embodiments, a (preferably compact) high-Q filter can befabricated using a MEMS resonator or an LC tank circuit, either of whichgenerally enables monolithic integration with CMOS circuits in designand manufacture; or using molecular resonance (though an LC tank circuitwill generally be significantly larger than a comparable ringoscillator). Those of ordinary skill in the art of integrated circuitoscillator circuit design will understand that various other high-Qresonance structures and materials can be used to provide a high-Qfilter as disclosed herein. For example, an on-chip LC tank can have a Qfactor of, e.g., 20 to 30; chip bond wires can have a Q factor of about50; a quartz crystal can have a Q factor in the millions; and an atomicclock resonance may have a Q factor in the trillions.

In some embodiments, a clock circuit as disclosed with respect to FIGS.1 and 3 can be used in minimal power mode (relatively higher phasenoise) to perform digital data processing, and in higher (but stillrelatively low) power mode (relatively lower phase noise) to perform RFtransmission. In some embodiments, the amount of power supplied to anoscillator circuit as disclosed with respect to FIGS. 1 and 3 isselected in dependence on an application-dependent tolerated level ofphase noise.

In some embodiments, multiple resonators with approximately the samecenter frequency can be used to filter a single frequency.

In some embodiments, resonators other than BAW resonators (e.g., othertypes of MEMS resonators) can be configured to cancel out thermal driftsin a beat frequency of said resonators.

As will be understood by those of ordinary skill in the art of art ofintegrated circuit oscillator circuit design, disclosure hereinregarding temperature-response matching of BAW resonators can be appliedto other resonators in which frequency response to temperature can becontrolled by modifying resonator structure.

In some embodiments as shown in FIGS. 6 and 8, high-Q resonators can beused which are not closely matched.

In some embodiments as shown in FIGS. 6 and 8, high-Q filters or high-Qresonators can be used which are not fabricated close to each other.

According to some but not necessarily all embodiments, there isprovided: A method of producing a clock signal, comprising the actionsof: a) producing, using an oscillator, a signal having a base frequencycomponent and an Nth harmonic component, wherein N is a selected integerand N>1; b) filtering said signal through a bandpass filter with Qfactor ≥5, said filter configured to pass said Nth harmonic component asa filtered Nth harmonic component; and c) injecting said filtered Nthharmonic component into said oscillator to thereby injection lock saidNth harmonic component of said signal to said filtered Nth harmoniccomponent, whereby said base frequency of said signal is self-injectionlocked.

According to some but not necessarily all embodiments, there isprovided: A self-injection locking clock circuit, comprising: a) anoscillator configured to output a periodic signal with at least a basefrequency and configured to injection lock to an injected signal; and b)a bandpass filter with Q factor ≥5, said filter configured to pass anNth harmonic of said base frequency to output a passed Nth harmonic, Nbeing an integer selected in at least partial dependence on said basefrequency and N>1, said filter operatively coupled to said oscillator tofilter said periodic signal and such that said passed Nth harmonic isinjected into said oscillator.

According to some but not necessarily all embodiments, there isprovided: A method of producing a clock signal, comprising the actionsof: a) producing, using an oscillator, a signal having a base frequencycomponent, an Mth harmonic component and a Pth harmonic component,wherein M and P are selected integers and M>P>1; b) filtering saidsignal through one or more bandpass filters comprising at least tworesonators, said filters having Q factor ≥5, said filters configured topass said Mth and Pth harmonic components as filtered Mth and Pthharmonic components, respectively; c) multiplying said filtered Mth andPth harmonic components together to produce a multiplied signal, andfiltering said multiplied signal using a low pass filter to pass adifference between said filtered Mth and Pth harmonic components, saiddifference comprising a filtered beat frequency waveform; and c)injecting said filtered beat frequency waveform into said oscillator tothereby injection lock said signal to said filtered beat frequencywaveform, whereby said base frequency of said signal is self-injectionlocked.

According to some but not necessarily all embodiments, there isprovided: A self-injection locking clock circuit, comprising: a) anoscillator configured to output a periodic signal with at least a basefrequency and configured to injection lock to an injected signal; b) oneor more bandpass filters with Q factor ≥5, said filters configured topass an Mth harmonic and a Pth harmonic of said base frequency to outputa filtered Mth harmonic and a filtered Pth harmonic, M and P beingintegers selected in at least partial dependence on said base frequencyand M>P>1, said filters operatively coupled to said oscillator to filtersaid oscillator output; c) a multiplier configured to multiply saidfiltered Mth harmonic by said filtered Pth harmonic to produce amultiplied Mth*Pth harmonic waveform having a beat frequency componentcomprising a difference between said filtered Mth harmonic and saidfiltered Pth harmonic; and d) a low pass filter configured to pass saidbeat frequency component as a filtered beat frequency component, suchthat said filtered beat frequency component is injected into saidoscillator.

According to some but not necessarily all embodiments, there isprovided: As disclosed herein, the inventors have discovered methods andsystems for producing a low-power, low-phase noise periodic oscillatingsignal using a self-injection locking oscillator. For example, anN-stage oscillator can be configured to receive an injected signal intoeach of the oscillator's N stages and connected in looped series with,optionally, a harmonic generator, and a high-Q filter. The high-Qfilter, preferably comprising a compact MEMS resonator, passes an Nthharmonic of the base frequency of the oscillator with a group delay. Thegroup-delayed Nth harmonic of the oscillator's base frequency isself-injected into the oscillator—that is, the oscillator's modifiedoutput is injected back into the oscillator. The oscillator output isinjection locked by the injected Nth harmonic to the oscillator's basefrequency. The oscillator's base frequency consequently injection locksto itself, with a slight change resulting from the group delay. Thissignificantly reduces phase noise in the injection locked oscillatoroutput signal (e.g., −30 dB).

According to some but not necessarily all embodiments, there isprovided: As disclosed herein, the inventors have discovered methods andsystems for producing a low-power, low-phase noise periodic oscillatingsignal using a self-injection locking oscillator. For example, anoscillator can be configured to receive an injected signal and connectedin looped series with a harmonic generator (optionally), two closelymatched high-Q bandpass filters, a multiplier, and a low pass filter.The high-Q filters, preferably comprising compact MEMS resonators, passMth and Pth harmonics of the base frequency of the oscillator with agroup delay. These signals are multiplied together and then fed into alow pass filter to produce a signal corresponding to the beat frequencyof—i.e., the difference between—the Mth and Pth harmonics. Thegroup-delayed beat frequency waveform is self-injected into theoscillator—that is, the oscillator's modified output is injected backinto the oscillator. The oscillator (the base frequency or a harmonic)locks to the injected beat frequency. The oscillator's base frequencyconsequently injection locks to itself, with a slight change resultingfrom the group delay. This significantly reduces phase noise in theinjection locked oscillator output signal (e.g., −32 dB). Also, becausethe closely matched high-Q filters respond identically to absolutedrifts and the oscillator injection locks to the difference betweenfilter output frequencies, absolute drifts are subtracted out. Further,the high-Q filters can be designed and fabricated to compensate for eachother's temperature drifts. As a result, the injection lockedoscillator's output is not only low phase noise, it is also highlyresilient against various types of time- and condition-dependent drift.

Additional general background, which helps to show variations andimplementations, may be found in the following publications (includingall of the references set forth hereinabove, which are repeated here),all of which are hereby incorporated by reference: L. Zhang, A.Daryoush, A. Poddar and U. Rohde, “Oscillator phase noise reductionusing self-injection locked and phase locked loop (SILPLL),” 2014 IEEEInternational Frequency Control Symposium (FCS), Taipei, 2014, pp. 1-4;Heng-Chia Chang, “Stability analysis of self-injection-lockedoscillators,” IEEE Transactions on Microwave Theory and Techniques, vol.51, no. 9, pp. 1989-1993, September 2003; Heng-Chia Chang, “Phase noisein self-injection-locked oscillators—theory and experiment,” IEEETransactions on Microwave Theory and Techniques, vol. 51, no. 9, pp.1994-1999, September 2003; X. Yi, C. C. Boon, M. A. Do, K. S. Yeo and W.M. Lim, “Design of Ring-Oscillator-Based Injection-Locked FrequencyDividers With Single-Phase Inputs,” IEEE Microwave and WirelessComponents Letters, vol. 21, no. 10, pp. 559-561, October 2011; and R.Nancollas, S. Bhattarai, “A Simulation Study of Injection LockedClocking with Ring Oscillators,”https://people.eecs.berkeley.edu/˜suchitb/EE241_MidTermReport, Mar. 21,2012, accessed Jun. 5, 2017; and B. Mesgarzadeh, Atila Alvandpour, “AStudy of Injection Locking in Ring Oscillators,” IEEE Symposium onCircuits and Systems, May 23-26, 2005.

None of the description in the present application should be read asimplying that any particular element, step, or function is an essentialelement which must be included in the claim scope: THE SCOPE OF PATENTEDSUBJECT MATTER IS DEFINED ONLY BY THE ALLOWED CLAIMS. Moreover, none ofthese claims are intended to invoke paragraph six of 35 USC section 112unless the exact words “means for” are followed by a participle.

The claims as filed are intended to be as comprehensive as possible, andNO subject matter is intentionally relinquished, dedicated, orabandoned.

As shown and described herein, the inventors have discovered a varietyof new and useful approaches to self-injection locking for low-powerlow-phase noise oscillators.

What is claimed is:
 1. A method of producing a clock signal, the methodcomprising: a) producing, using an oscillator, a signal having a basefrequency component and an Nth harmonic component, wherein N is aninteger, and N>1; b) filtering the signal through a bandpass filter, inwhich the bandpass filter has Q factor ≥5 and passes the Nth harmoniccomponent as a filtered Nth harmonic component; and c) injecting thefiltered Nth harmonic component into the oscillator to self-injectionlock the base frequency of the signal.
 2. The method of claim 1, whereinthe base frequency is between 200 MHz and 1 GHz.
 3. The method of claim1, wherein N is an odd number ≥3.
 4. The method of claim 1, wherein theproducing includes using a harmonic generator to generate the signalusing an output of the oscillator.
 5. The method of claim 1, wherein theoscillator is a ring oscillator including N stages, and the injectingincludes injecting the filtered Nth harmonic component into each of theN stages.
 6. The method of claim 1, further comprising inducing a groupdelay in the Nth harmonic component of the signal using the bandpassfilter.
 7. The method of claim 1, wherein the N, the Q factor, and anamplitude of the Nth harmonic component are sufficient to produce aphase noise reduction in an injection locked output of the oscillatorwith respect to a free running output of the oscillator.
 8. The methodof claim 1, further comprising selecting the N, including by selectingwhich of multiple filters is used to perform the step b).
 9. The methodof claim 1, further comprising adjusting properties of the oscillator toselect the base frequency of the oscillator between different iterationsof the steps a) through c).
 10. The method of claim 1, wherein the basefrequency component of the signal when the oscillator is free runninghas a different frequency from the base frequency component of thesignal when the oscillator is injection locked.
 11. A self-injectionlocking clock circuit, comprising: a) an oscillator configured to outputa periodic signal with at least a base frequency and configured toinjection lock to an injected signal; and b) a bandpass filter having Qfactor ≥5, the bandpass filter configured to pass an Nth harmonic of thebase frequency to output a filtered Nth harmonic, N being an integer atleast partially dependent on the base frequency, in which N>1, and thebandpass filter is operatively coupled to the oscillator and configuredto filter the periodic signal to inject the filtered Nth harmonic intothe oscillator.
 12. The circuit of claim 11, wherein the oscillator is aring oscillator.
 13. The circuit of claim 12, wherein the ringoscillator includes N inverters.
 14. The circuit of claim 13, wherein Nis an odd number.
 15. The circuit of claim 11, wherein the bandpassfilter includes a MEMS resonator or an LC tank.
 16. The circuit of claim11, wherein the bandpass filter includes a bulk acoustic wave resonator.17. The circuit of claim 11, wherein the oscillator is an N-stageoscillator.
 18. The circuit of claim 11, further comprising a harmonicgenerator which generates the Nth harmonic using the periodic signal.19. The circuit of claim 11, wherein the bandpass filter includesmultiple filters configured to respectively pass different Nth harmoniesof the base frequency, and the circuit further comprises a selectorconfigured to select which of the multiple filters outputs the filteredNth harmonic.
 20. The circuit of claim 11, wherein the oscillator isconfigured to adjust a base frequency of the oscillator in at leastpartial dependence on a signal from outside the circuit.